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Movement on a sphere (elliptic integrals)

  1. Apr 10, 2009 #1
    1. The problem statement, all variables and given/known data
    A point moves with constant speed (value) over a sphere, following the curve defined by: f = t = l
    For t=0, the point is at (t,f) = (0,0) and for t=3 it's at (pi/4, pi/4).
    How long does it take to reach the north pole of the sphere?

    2. Relevant equations
    The parametric equations for this sphere are:
    x = 5·cos f·cos t
    y = 5·cos f·sin t
    z = 5·sin f

    3. The attempt at a solution
    OK first of all, the parametric equations turn into:
    x = 5·cos2 l
    y = 5·cos l·sin l
    z = 5·sin l

    Then we know that:
    v2 = x'2 + y'2 + z'2
    So we find:
    x' = -5·sin(2l)
    y' = 5·cos(2l)
    z' = 5·cos l

    By adding them up, we simplify the squared sines-cosines:
    v2 = 25(1 + ·cos2 l)·(dl/dt)2
    v·dt = 5√(1 + ·cos2 l)·dl

    However I don't know how to find v, and I'm not sure this is correct so far.

    Thank you for your help
     
  2. jcsd
  3. Apr 14, 2009 #2
    Bump...
     
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